Question: Jessica is 15 years older than Ben. Fifteen years ago, Jessica was 4 times as old as Ben. How old is Ben now?
Explanation: We can use the given information to write down two equations that describe the ages of Jessica and Ben. Let Jessica's current age be $j$ and Ben's current age be $b$ The information in the first sentence can be expressed in the following equation: $j = b + 15$ Fifteen years ago, Jessica was $j - 15$ years old, and Ben was $b - 15$ years old. The information in the second sentence can be expressed in the following equation: $j - 15 = 4(b - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = b + 15$ . Substituting this into our second equation, we get the equation: $(b + 15)$ $-$ $15 = 4(b - 15)$ which combines the information about $b$ from both of our original equations. Simplifying both sides of this equation, we get: $b + 0 = 4 b - 60$ Solving for $b$ , we get: $3 b = 60$ $b = 20$.